ocean biogeochemistry and ecology, modeling of

OCEAN BIOGEOCHEMISTRY AND ECOLOGY,MODELING OF

N. Gruber, Institute of Biogeochemistry and PollutantDynamics, ETH Zurich, SwitzerlandS. C. Doney, Woods Hole Oceanographic Institution,Woods Hole, MA, USA

& 2009 Elsevier Ltd. All rights reserved.

Introduction

Modeling has emerged in the last few decades as acentral approach for the study of biogeochemical andecological processes in the sea. While this develop-ment was facilitated by the fast development ofcomputer power, the main driver is the need toanalyze and synthesize the rapidly expanding obser-vations, to formulate and test hypotheses, and tomake predictions how ocean ecology and bio-geochemistry respond to perturbations. The finalaim, prediction, has gained in importance recentlyas scientists are increasingly asked by society to in-vestigate and assess the impact of past, current, andfuture human actions on ocean ecology andbiogeochemistry.

The impact of the carbon dioxide (CO2) that hu-mankind has emitted and will continue to emit intothe atmosphere for the foreseeable future is currently,perhaps, the dominant question facing the marinebiogeochemical/ecological research community. Thisimpact is multifaceted, and includes both direct (suchas ocean acidification) and indirect effects that areassociated with the CO2-induced climate change. Ofparticular concern is the possibility that global cli-mate change will lead to a reduced capacity of theocean to absorb CO2 from the atmosphere, so that alarger fraction of the CO2 emitted into the atmos-phere remains there, further enhancing globalwarming. In such a positive feedback case, the ex-pected climate change for a given CO2 emission willbe larger relative to a case without feedbacks. Mar-ine biogeochemical/ecological models have played acrucial role in elucidating and evaluating these pro-cesses, and they are increasingly used for makingquantitative predictions with direct implications forclimate policy.

There are many other marine biogeochemical and/or ecological problems related to human activities,for which models play a crucial role assessing theirimportance and magnitude and devising possible

solutions. These include, for example, coastal eu-trophication, overfishing, and dispersion of invasivespecies. The use of marine biogeochemical/ecologicalmodels is now so pervasive that practically everyfield of oceanography is on this list.

The aim of this article is to provide an intro-duction and overview of marine biogeochemical andecological modeling. Given the breadth of modelingapproaches in use today, this overview can by designnot be inclusive and authoritative. We rather focuson some basic concepts and provide a few illustrativeapplications. We start with a broader description ofthe marine biogeochemical/ecological challenge athand, and then introduce basic concepts used forbiogeochemical/ecological modeling. In the finalsection, we use a number of examples to illustratesome of the core modeling approaches.

The Marine Ecology andBiogeochemistry Challenge

The complexity of the ocean biogeochemical/eco-logical problem is daunting, as it involves a complexinterplay among biology, physical variability of theoceanic environment, and the interconnected cyclesof a large number of bioactive elements, particularlythose of carbon, nitrogen, phosphorus, oxygen, sil-icon, and iron (Figure 1). Furthermore, the ocean isan open system that exchanges mass and manyelements with the surrounding realms, such as theatmosphere, the land, and the sediments.

The engine that sets nearly all of these cycles intomotion is the photosynthetic fixation of dissolvedinorganic carbon and many other nutrient elementsinto organic matter by phytoplankton in the illu-minated upper layers of the ocean (euphotic zone).The net rate of this process (i.e., net primary pro-duction) is distributed heterogeneously in the ocean,primarily as a result of the combined limitation ofnutrients and light. This results in similar hetero-geneity in surface chlorophyll, a direct indicator ofthe amount of phytoplankton biomass (Figure 2(a)).The large-scale surface nutrient distributions, in turn,reflect the balance between biological removal andthe physical processes of upwelling and mixing thattransport subsurface nutrient pools upward into theeuphotic zone (Figure 2(b)). In addition to the tra-ditional macronutrients (nitrate, phosphate, silicateetc.), growing evidence shows that iron limitation is

89

Atmosphere

Sediments

Ocean

Eup

hotic

zon

eA

phot

ic z

one

DIC

Org. matter

Org. matter

DIC

CO2

NO3

N2

N2

N2O

N2O

O2

O2

O2

PO4

PO4

SiO4

SiO2

SiO2

SiO4

4-

4-

CaCO3

CaCO3

SiO2 Org. matterCaCO3

DIC

CalcificationN2-fixation

Settling

Denitrification

Mixing/circulation

Air−sea gas exchangeAir−sea gas exchange

Settling

Settling

Silification

N2O

NO3

NO3

PO4

Mixing/circulation

Mixing/circulationN2

Figure 1 Schematic diagram of a number of key biogeochemical cycles in the ocean and their coupling. Shown are the cycles of

carbon, oxygen, phosphorus, nitrogen, and silicon. The main engine of most biogeochemical cycles in the ocean is the biological

production of organic matter in the illuminated upper ocean (euphotic zone), part of which sinks down into the ocean’s interior and is

then degraded back to inorganic constituents. This organic matter cycle involves not only carbon, but also nitrogen, phosphorus, and

oxygen, causing a tight linkage between the cycles of these four elements. Since some phytoplankton, such as diatoms and

coccolithophorids, produce shells made out of amorphous silicon and solid calcium carbonate, the silicon and CaCO3 cycles also tend

to be closely associated with the organic matter cycle. These ocean interior cycles are also connected to the atmosphere through the

exchange of a couple of important gases, such as CO2, oxygen, and nitrous oxide (N2O). In fact, on timescales longer than a few

decades, the ocean is the main controlling agent for the atmospheric CO2 content.

90 OCEAN BIOGEOCHEMISTRY AND ECOLOGY, MODELING OF

a key factor governing net primary production inmany parts of the ocean away from the main ex-ternal sources for iron, such as atmospheric dustdeposition and continental margin sediments. Thephotosynthesized organic matter is the basis for acomplex food web that involves both a transfer ofthe organic matter toward higher trophic levels aswell as a microbial loop that is responsible for mostof the breakdown of this organic matter back to itsinorganic constituents.

A fraction of the synthesized organic matter (about10–20%) escapes degradation in the euphotic zoneand sinks down into the dark aphotic zone, where itfuels the growth of microbes and zooplankton thateventually also remineralize most of this organicmatter back to its inorganic constituents. The nutrientelements and the dissolved inorganic carbon are theneventually returned back to the surface ocean byocean circulation and mixing, closing this ‘great bio-geochemical loop’. This loop is slightly leaky in that a

small fraction of the sinking organic matter fails to getremineralized in the water column and is depositedonto the sediments. Very little organic matter escapesremineralization in the sediments though, so that onlya tiny fraction of the organic matter produced in thesurface is permanently removed from the ocean bysediment burial. In the long-term steady state, this lossof carbon and other nutrient elements from the oceanis replaced by the input from land by rivers andthrough the atmosphere.

Several marine phytoplankton and zooplanktongroups produce hard shells consisting of either min-eral calcium carbonate (CaCO3) or amorphous sil-ica, referred to as ‘opal’ (SiO2). The most importantproducers of CaCO3 are coccolithophorids, whilemost marine opal stems from diatoms. Both groupsare photosynthetic phytoplankton, highlighting theextraordinary importance of this trophic group formarine ecology and biogeochemistry. Upon the deathof the mineral-forming organisms, these minerals

GM 50° E 160° W150° E100° E 60° W110° W50° W

80° S

Eq.

40° S

80° N

40° N

80° S

Eq.

40° S

80° N

40° N

80° S

Eq.

40° S

80° N

40° N

Chlorophyll (mg Chl m−3)

Nitrate (mmol m−3)

Sea-to-air CO2 flux (mol m−2 yr −1)

(a)

(b)

(c)

2

1.5

1

0.5

0.4

0.3

0.2

0.1

0.08

0.06

0.04

0.02

0

34323028262422201816141210

1054.543.5

2.5

1.5

3

2

0

−1−0.5

−1.5−2−2.5−3

−4−4.5−5−10

−3.5

10.5

86421

Figure 2 Global maps of the distribution of three key biogeochemical/ecological modeling targets. (a) Annual mean distribution of

near-surface chlorophyll (mg Chl m� 3) as measured by the SeaWiFS satellite. (b) Annual mean surface distribution of nitrate

(mmol� 3) compiled from in situ observations (from the World Ocean Atlas). (c) Annual mean air–sea CO2 flux (mol m� 2 yr� 1) for a

nominal year of 2000 derived from a compilation of in situ measurements of the oceanic pCO2 and a wind-speed gas exchange

parametrization. Data provided by T. Takahashi, Lamont Doherty Earth Observatory of Columbia University.

OCEAN BIOGEOCHEMISTRY AND ECOLOGY, MODELING OF 91

also sink into the ocean’s interior, thereby oftenacting as ‘ballast’ for organic matter.

This great biogeochemical loop also has a strongimpact on several gases that are dissolved in seawater

and exchange readily with the atmosphere, mostimportantly CO2 and oxygen (O2). Biological pro-cesses have opposite effects on these two gases:photosynthesis consumes CO2 and liberates O2,


while respiration and bacterial degradation releasesCO2 and consumes O2. As a result, one tends to findan inverse relationship in the oceanic distribution ofthese two gases. CO2 also sets itself apart from O2 inthat it reacts readily with seawater. In fact, due to thehigh content of alkaline substances in the ocean, thisreaction is nearly complete, so that only around 1%of the total dissolved inorganic carbon in the oceanexists in the form of CO2.

The exchange of CO2 across the air–sea interfaceis a prime question facing ocean biogeochemical/ecological research, particularly with regard to themagnitude of the oceanic sink for anthropogenicCO2. The anthropogenic CO2 sink occurs on top ofthe natural air–sea CO2 fluxes characterized byoceanic uptake in mid-latitudes and some high lati-tudes, and outgassing in the low latitudes and theSouthern Ocean. This distribution of the naturalCO2 flux is the result of an interaction between theexchange of heat between the ocean and the atmos-phere, which affects the solubility of CO2, and thegreat biogeochemical loop, which causes an uptakeof CO2 from the atmosphere in regions where thedownward flux of organic carbon exceeds the up-ward supply of dissolved inorganic carbon, and anoutgassing where the balance is the opposite. Thisflux has changed considerably over the last twocenturies in response to the anthropogenically drivenincrease in atmospheric CO2 that pushes additionalCO2 from the atmosphere into the ocean. Never-theless, the pattern of the resulting contemporaryair–sea CO2 flux (Figure 2(c)) primarily still reflectsthe flux pattern of the natural CO2 fluxes, albeit witha global integral flux into the ocean reflecting theoceanic uptake of anthropogenic CO2.

Given the central role of the great biogeochemicalloop, any modeling of marine biogeochemical/eco-logical processes invariably revolves around themodeling of all the processes that make up this loop.As this loop starts with the photosynthetic pro-duction of organic matter by phytoplankton, bio-geochemical modeling is always tightly interwovenwith the modeling of marine ecology, especially thatof the lower trophic levels.

Core questions that challenge marine bio-geochemistry and ecology are as follows:

1. What controls the mean concentration and three-dimensional (3-D) distribution of bioreactiveelements in the ocean?

2. What controls the air–sea balance of climaticallyimportant gases, that is, CO2, N2O, and O2?

3. What controls ocean productivity, the downwardexport of organic matter, and the transfer of or-ganic matter to higher trophic levels?

4. How do ocean biogeochemistry and ecologychange in time in response to climate dynamicsand human perturbations?

Modeling represents a powerful approach tostudying and addressing these core questions. Mod-eling is by no means the sole approach. In fact,integrated approaches that combine observational,experimental, and modeling approaches are oftennecessary to tackle this set of complex problems.

What Is a Biogeochemical/EcologicalModel?

At its most fundamental level, a model is an abstractdescription of how some aspect of nature functions,most often consisting of a set of mathematical ex-pressions. In the biogeochemical/ecological modelingcontext, a model usually consists of a number ofpartial differential equations, which describe thetime and space evolution of a (limited) number ofecological/biogeochemical state variables. As few ofthese equations can be solved analytically, they areoften solved numerically using a computer, whichrequires the discretization of these equations, that is,they are converted into difference equations on apredefined spatial and temporal grid.

The Art of Biogeochemical/EcologicalModeling

A model can never fully represent reality. Rather, itaims to represent an aspect of reality in the contextof a particular problem. The art of modeling is tofind the right level of abstraction, while keepingenough complexity to resolve the problem at hand.That is, marine modelers often follow the strategy ofOccam’s razor, which states that given two com-peting explanations, the one that is simpler andmakes fewer assumptions is the more likely to becorrect. Therefore, a typical model can be used onlyfor a limited set of applications, and great care mustbe used when a model is applied to a problem forwhich it was not designed. This is especially truefor biogeochemical/ecological models, since theirunderlying mathematical descriptions are for themost part not based on first principles, but oftenderived from empirical relationships. In fact, marinebiogeochemical/ecological modeling is at present adata-limited activity because we lack data to for-mulate and parametrize key processes and/or toevaluate the model predictions. Further, significantsimplifications are often made to make the problemmore tractable. For example, rather than treating


individual organisms or even species, model vari-ables often aggregate entire functional groups intosingle boxes (e.g., photosynthetic organisms, grazers,and detritus decomposers), which are then simulatedas bulk concentrations (e.g., mol C m�3 of phyto-plankton).

Despite these limitations, models allow us to askquestions about the ocean inaccessible from data orexperiments alone. In particular, models help re-searchers quantify the interactions among multipleprocesses, synthesize diverse observations, test hy-potheses, extrapolate across time – space scales, andpredict past and future behavior. A well-posed modelencapsulates our understanding of the ocean in amathematically consistent form.

Biogeochemical/Ecological ModelingEquations and Approaches

In contrast with their terrestrial counterparts, modelsof marine biogeochemical/ecological processes mustbe coupled to a physical circulation model of somesort to take into consideration that nearly all relevantbiological and biogeochemical processes occur eitherin the dissolved or suspended phase, and thus aresubject to mixing and transport by ocean currents.Thus, a typical coupled physical–biogeochemical/ecological model consists of a set of time-dependentadvection, diffusion, and reaction equations:

@C

@tþ AdvðCÞ þDiffðCÞ ¼ SMSðCÞ ½1�

where C is the state variable to be modeled, such asthe concentration of phytoplankton, nutrients, ordissolved inorganic carbon, often in units of mass perunit volume (e.g., mol m� 3). Adv(C) and Diff(C) arethe contributions to the temporal change in C byadvection and eddy-diffusion (mixing), respectively,derived from the physical model component.The term SMS(C) refers to the ‘sources minussinks’ of C driven by ecological/biogeochemicalprocesses. The SMS term often involves complexinteractions among a number of state variables and isprovided by the biogeochemical/ecological modelcomponent.

Marine biogeochemical/ecological models are di-verse, covering a wide range of complexities andapplications from simple box models to globally 4-D-(space and time) coupled physical–biogeochemicalsimulations, and from strict research tools to climatechange projections with direct societal implications.Model development and usage are strongly shaped bythe motivating scientific or policy problems as well asthe dynamics and time–space scales considered. The

complexity of marine biogeochemical/ecologicalmodels can be organized along two major axes(Figure 3): the physical complexity, which determineshow the left-hand side of [1] is computed, and thebiogeochemical/ecological complexity, which deter-mines how the right-hand side of [1] is evaluated.

Due to computational and analytical limitations,there is often a trade-off between the physical andbiogeochemical/ecological complexity, so that mod-els of the highest physical complexity are often usingrelatively simple biogeochemical/ecological modelsand vice versa (Figure 4). Additional constraintsarise from the temporal domain of the integrations.Applications of coupled physical–biogeochemical/ecological models to paleoceanographic questionsrequire integrations of several thousand years.This can only be achieved by reducing both thephysical and the biogeochemical/ecological com-plexity (Figure 4). At the same time, the continuouslyincreasing computational power has permitted re-searchers to push forward along both complexityaxes. Nevertheless, the fundamental tradeoff be-tween physical and biogeochemical/ecological com-plexity remains.

In addition to the physical and biogeochemical/ecological complexity, models can also be categor-ized with regard to their interaction with obser-vations. In the case of ‘forward models’, a set ofequations in the form of [1] is integrated forward intime given initial and boundary conditions. A typicalforward problem is the prediction of the future stateof ocean biogeochemistry and ecology for a certainevolution of the Earth’s climate. The solutions ofsuch forward models are the time–space distributionof the state variables as well as the implied fluxes.The expression ‘inverse models’ refers to a broadpalette of modeling approaches, but all of them sharethe goal of optimally combining observations withknowledge about the workings of a system as em-bodied in the model. Solutions to such inversemodels can be improved estimates of the currentstate of the system (state estimation), improved es-timates of the initial or boundary conditions,or an optimal set of parameters. A typical example ofan inverse model is the optimal determination ofecological parameters, such as growth andgrazing rates, given, for example, the observed dis-tribution of phytoplankton, zooplankton, andnutrients.

Examples

Given the large diversity of marine biogeochemical/ecological models and approaches, no review can do

box 1-D 2-D 3-D 3-D (eddy resolving)

NP NPZD NiPjZkBlDmN

Variable stoichiometry

Fixed stoichiometry

Biogeochemical/ecological complexity Higher complexity

Upper ocean ecology (lower trophic levels)

ZFUpper ocean ecology (higher trophic levels)

Elemental coupling

Other reservoirs

Ocean only

Sediments passive

Sediments active

Aphotic zone processes

Implicit remineralization

Sinking particles with parametrized remineralization

Sinking particles with aphotic ecosystem determining remineralization

NPZBD

ZF with life cycles

ZFn with life cycles and coupled to lower trophic level model

Physiological modeling

Physical complexity Higher complexity

Spatial resolution

System coupling

ocean only

ocean/ sea-ice

ocean/ sea-ice/ atmosphere/ land surface

Figure 3 Schematic diagram summarizing the development of complexity in coupled physical–biogeochemical/ecological models.

The two major axes of complexity are biogeochemistry/ecology and physics, but each major axis consists of many subaxes that

describe the complexity of various subcomponents. Currently existing models fill a large portion of the multidimensional space opened

by these axes. In addition, the evolution of models is not always necessarily straight along any given axis, but depends on the nature of

the particular problem investigated. N, nutrient; P, phytoplankton; Z, zooplankton; B, bacteria; D, detritus; F, fish.


full justice. We restrict our article here to the dis-cussion of four examples, which span the range ofcomplexities as well as have been important mile-stones in the evolution of biogeochemical/ecologicalmodeling.

Box Models or What Controls Atmospheric CarbonDioxide?

Our aim here is to develop a model that explains howthe great biogeochemical loop controls atmosphericCO2. The key to answering this question is a quanti-tative prediction of the surface ocean concentration of

CO2, as it is this surface concentration that controlsthe atmosphere–ocean balance of CO2. The simplestmodels used for such a purpose are box models, wherethe spatial dimension is reduced to a very limitednumber of discrete boxes. Such box models haveplayed an important role in ocean biogeochemical/ecological modeling, mostly because their solutionscan be readily explored and understood. However,due to the dramatic reduction of complexity, there arealso important limitations, whose consequences onemust keep in mind when interpreting the results.

Box models can be formally derived from thetracer conservation eq [1] by integrating over

Bio

geoc

hem

ical

/eco

logi

cal c

ompl

exity

Hig

her

com

plex

ity

Physical complexity Higher complexity

Geochemical applications long-term integrations

Temporal evolution Physical−biological

coupling studiesshort-term integrations

Climate-change studies century-timescale integrations

Ecological case studies (e.g., test-beds) short-term integrations

Incre

asing

CPU tim

e

per

grid

point

and t

empo

ral d

omain

Figure 4 Schematic illustrating the relationship between the physical (abscissa) and the biogeochemical/ecological complexity

(ordinate) of different typical applications of coupled physical–biogeochemical/ecological models. Given computational and analytical

constraints, there is often a trade-off between the two main complexities. The thin lines in the background indicate the CPU time

required for the computation of a problem over a given time period.


the volume of the box, V, and by applying Gauss’(divergence) theorem, which states that the volumeintegral of a flux is equal to the flux in normal dir-ection across the boundary surfaces, S. The resultingintegral form of [1] is:

Z@C

@tdV þ

IAdvnðCÞ þDiffnðCÞð Þ dS

¼Z

SMSðCÞ dV ½2�

where Advn(C) and Diffn(C) are the advective anddiffusive transports in the normal direction across S.If we assume that the concentration of tracer C aswell as the SMS term within the box are uniform, [2]

can be rewritten as

V � dC

dtþX

i

Ti;out � C� Ti;in � Ci þ niðC� CiÞ� �

¼ V � SMSðCÞ ½3�

where C is the mean concentration within the box.We represented the advective contributions as prod-ucts of a mass transport, T (dimensions volumetime� 1), with the respective upstream concentration,separately considering the mass transport into thebox and out of the box across each interface i, that is,Ti,in and Ti,out. The eddy-diffusion contributionsare parametrized as products of a mixing coefficient,ni (dimension volume time� 1), with the gradient


across each interface ðC� CiÞ. For simplicity, wesubsequently drop the overbar, that is, use C insteadof C.

The simplest box-model representation of thegreat biogeochemical loop is a two-box model,wherein the ocean is divided into a surface and adeep box, representing the euphotic and aphoticzones, respectively (Figure 5(a)). Mixing and trans-port between the two boxes is modeled with a mix-ing term, n. The entire complexity of marine ecologyand biogeochemistry in the euphotic zone is reducedto a single term, F, which represents the flux of or-ganic matter out of the surface box and into the deepbox, where the organic matter is degraded back toinorganic constituents.

Let us consider the deep-box balance for a dis-solved inorganic bioreactive element, Cd (such asnitrate, phosphate, or dissolved inorganic carbon):

VddCd

dtþ n � ðCd � CsÞ ¼ F ½4�

where Vd is the volume of the deep box and Cs is thedissolved inorganic concentration of the surface box.The steady-state solution of [4], that is, the solutionwhen the time derivative of Cd vanishes (dCd/dt¼ 0),

n � ðCd � CsÞ ¼ F ½5�

represents the most fundamental balance of the greatbiogeochemical loop. It states that the net upwardtransport of an inorganic bioreactive element byphysical mixing is balanced by the downwardtransport of this element in organic matter. Thissteady-state balance [5] has several important ap-plications. For example, it permits us to estimate thedownward export of organic matter by simply

Surface

Deep

Φ ν

Cd

Cs

Vd

Vs

Tw

o-bo

x m

odel

(a)

Figure 5 Schematic representation of the great biogeochemical

C, concentrations; V, volume; n, exchange (mixing) coefficient; F, o

analyzing the vertical gradient and by estimating thevertical exchange. The balance also states that themagnitude of the vertical gradient in bioreactiveelements is proportional to the strength of thedownward flux of organic matter and inverselyproportional to the mixing coefficient. Since nearlyall oceanic inorganic carbon and nutrients reside inthe deep box, that is, Vd � CdcVs � Cs, one can as-sume, to first order, that Cd is largely invariant, sothat the transformed balance for the surface oceanconcentration

Cs ¼ Cd �Fn

½6�

reveals that the surface concentration depends pri-marily on the relative magnitude of the organicmatter export to the magnitude of vertical mixing.Hence, [6] provides us with a first answer to ourchallenge: it states that, for a given amount of oceanmixing, the surface ocean concentration of inorganiccarbon, and hence atmospheric CO2, will decreasewith increasing marine export production. Rela-tionship [6] also states that for a given magnitude ofmarine export production, atmospheric CO2 willincrease with increased mixing.

While very powerful, the two-box model has se-vere limitations. The most important one is that thismodel does not consider the fact that the deep oceanexchanges readily only with the high latitudes, whichrepresent only a very small part of the surface ocean.The exchange of the deep ocean with the low lati-tudes is severly limited because diapcyncal mixing inthe ocean is small. Another limitation is that the one-box model does not take into account that the nu-trient concentrations in the high latitudes tend to bemuch higher than in the low latitudes (Figure 2(c)).

Deep

Low-latHigh-lat

T

�hdΦl

ΦhCd

C l

Ch

Vd

Vh

Vl

Thr

ee-b

ox m

odel

(b)

loop in box models: (a) two-box model and (b) three-box model.

rganic matter export fluxes; T, advective transport.

Window open

33 0

33

Atmospheric pCO2 (ppm)

425

Preindustrial

26 0

33

280

Window closed

00

33

160

� = +145 � = −120

Nitrate balance (mmol−3)

(a) (b) (c)

Figure 6 Schematic illustration of the impact of the high-latitude (Southern Ocean) window on atmospheric CO2. In (a) the high-

latitude window is open, high-latitude nitrate is high, and atmospheric CO2 attains 425 ppm. Panel (b) represents the preindustrial

ocean, where the window is half open, nitrate in the high latitudes is at intermediate levels, and atmospheric CO2 is 280 ppm. In (c), the

high-latitude window is closed, high-latitude nitrate is low, and atmospheric CO2 decreases to about 160 ppm.


An elegant solution is the separation of the surfacebox into a high-latitude box, h, and a low-latitudebox, l (Figure 5(b)). Intense mixing is assumed tooccur only between the deep and the high-latitudeboxes, nhd. A large-scale transport, T, is added tomimic the ocean’s global-scale overturning circu-lation. As before, the complex SMS terms are sum-marized by Fl and Fh. In steady state, the surfaceconcentrations are given by

Cl ¼ Cd �Fl

T

Ch ¼ Cd �Fh þ Fl

T þ nhd

½7�

which are structurally analogous to [6], but em-phasize the different dynamics setting balances in thelow and high latitudes. With nhdcT and FlEFh, [7]explains immediately why nutrient concentrationstend to be higher in high latitudes than in low lati-tudes (Figure 2(b)). In fact, writing [7] out for bothnitrate ðNO�3 Þ and dissolved inorganic carbon (DIC),and using the observation that surface NO�3 in thelow latitudes is essentially zero (Figure 2(c)), the DICequations are

DICl ¼ DICd � rC:N � ½NO�3 �d

DICh ¼ DICd �Fh þ rC:N � T � ½NO�3 �d

T þ nhd

½8�

where rC:N is the carbon-to-nitrogen ratio of organicmatter. Assuming that the deep-ocean nitrate con-centration is time invariant, the analysis of [8] re-veals that the low-latitude DIC concentration, DICl,

is more or less fixed, while the high-latitude DICconcentration, DICh, can be readily altered bychanges in either the high-latitude export flux, Fh, orhigh-latitude mixing, nhd. Furthermore, if one con-siders the fact that the rapid communication betweenthe high-latitude ocean and the deep ocean makes thehigh latitudes the primary window into the oceanicreservoir of inorganic carbon, it becomes clear that itmust be the high latitudes that control atmosphericCO2 on the millenial timescales where the steady-state approximation is justified. This high-latitudedominance in controlling atmospheric CO2 is illus-trated in Figure 6, which demonstrates that atmos-pheric CO2 can vary between about 160 and425 ppm by simply opening or closing this high-latitude window. The exact magnitude of the at-mospheric CO2 change depends, to a substantialdegree, on the details of the model, but the domin-ance of high-latitude processes in controlling at-mospheric CO2 is also found in much more complexand spatially explicit models. As a result, a change inthe carbon cycle in the high latitudes continues to bethe leading explanation for the substantially loweratmospheric CO2 concentrations during the ice ages.

NP and NPZ Models, or What Simple EcosystemModels Can Say about Oceanic Productivity

So far, we have represented the ecological, chemical,and physical processes that control the production oforganic matter and its subsequent export with asingle parameter, F. Clearly, in order to assesshow marine biology responds to climate change andother perturbations, it is necessary to resolve these


processes in much more detail. Two fundamentallydifferent approaches have been developed to modelsuch ecological processes: concentration-basedmodels and individually based models (IBMs). In thelatter, the model’s equations represent the growthand losses of individual organisms, and the modelthen simulates the evolution of a large number ofthese individuals through space and time. This ap-proach is most commonly used for the modeling oforganisms at higher trophic levels, where life cyclesplay an important role (e.g., models of zooplankton,fish, and marine mammals). In contrast, concen-tration-based models are almost exclusively used forthe modeling of the lower trophic levels, in particularto represent the interaction of light, nutrient, andgrazing in controlling the growth of phytoplankton,that is, marine primary production.

The simplest such model considers just one limit-ing nutrient, N, and one single phytoplankton group,P (see also Figure 7(a)):

SMSðPÞ ¼ Vmax �N

KN þN� P� lP � P

SMSðNÞ ¼ �Vmax �N

KN þN� Pþ mP � lP � P

½9�

where the first term on the right-hand side of thephytoplankton eqn [9] is net phytoplankton growth(equal to net primary production) modeled here as afunction of a nutrient-saturated growth rate Vmax,and a hyperbolic dependence on the in situ nutrientconcentration (Monod-type), with a single para-meter, the half-saturation constant, KN. The secondterm is the net loss due to senescence, viral infection,and grazing, modeled here as a linear process with aloss rate lP. A fraction mP of the phytoplankton lossis assumed to be regenerated inside the euphoticzone, while a fraction (1� mP) is exported to depth(Figure 7(a)). These two parametrizations forphytoplankton growth and losses reflect a typicalsituation for marine ecosystem models in that thegrowth terms are substantially more elaborate, re-flecting the interacting influence of various control-ling parameters, whereas the loss processes arehighly simplified. This situation also reflects the factthat the processes controlling the growth of marineorganisms are often more amenable to experimentalstudies, while the loss processes are much harder toinvestigate with careful experiments.

When the SMS terms of [10] are inserted into thefull tracer conservation eqn [1], the resulting equa-tions form a set of coupled partial differential equa-tions with a number of interesting consequences insteady state as shown in Figure 8(a). Below a certainnutrient concentration threshold, phytoplankton

growth is smaller than its loss term, so that the re-sulting steady-state solution is P¼ 0, that is, nophytoplankton. Above this threshold, the abundanceof phytoplankton (and hence primary production)increases with increasing nutrient supply in a linearmanner. Phytoplankton is successful in reducing thedissolved inorganic nutrient concentration to lowlevels, so that the steady state is characterized by mostnutrients residing in organic form in the phyto-plankton pool. This NP model reflects a situationwhere marine productivity is limited by bottom-upprocesses, that is, the supply of the essential nutrients.Comparison with the nutrient and phytoplanktondistribution shown in (Figure 2(b)) shows that thismodel could explain the observations in the sub-tropical open ocean, where nutrients are indeeddrawn down to very low levels. However, the NPmodel would also predict relatively high P levels to goalong with the low nutrient levels, which is clearly notobserved (Figure 2(a)). In addition, this NP modelalso fails clearly to explain the high-nutrient regionsof the high latitudes. However, we have so far neg-lected the limitation by light, as well as the impact ofzooplankton grazing.

The addition of a zooplankton compartment tothe NP model (Figure 7(b)) dramatically shifts thenutrient allocation behavior (Figure 8(b)). In thiscase, as the nutrient loading increases, the phyto-plankton abundance gets capped at a certain level byzooplankton grazing. Due to the reduced levels ofbiomass, the phytoplankton is then no longer able toconsume all nutrients at high-nutrient loads, so thatan increasing fraction of the supplied nutrients re-mains unused. This top-down limitation situationcould therefore, in part, explain why macronutrientsin certain regions remain untapped. Most recentresearch suggests that micronutrient (iron) limi-tation, in conjunction with zooplankton grazing,plays a more important role in causing these high-nutrient/low chlorophyll regions. Another key limi-tation is light, which has important consequences forthe seasonal and depth evolution of phytoplankton.

Global 3-D Modeling of Ocean Biogeochemistry/Ecology

The coupling of relatively simple NPZ-type modelsto global coarse-resolution 3-D circulation modelshas proven to be a challenging task. Perhaps the mostimportant limitation of such NPZ models is the factthat all phytoplankton in the ocean are representedby a single phytoplankton group, which is grazedupon by a single zooplankton group. This means thatthe tiny phytoplankton that dominate the relativelynutrient-poor central gyres of the ocean, and the

Phytoplankton(P )

DIN + DON(N )

Zooplankton(Z )

N−P model

(a)

Phytoplankton(P)

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P · Vmax · NKN + N

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respiration and egestion

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Rem

iner

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n

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iner

aliz

atio

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eral

izat

ion

g · Z · P

g · Z · P

Figure 7 A schematic illustration of (a) a nitrate–phytoplankton model and (b) a nitrate–phytoplankton–zooplankton model. The

mathematical expressions associated with each arrow represent typical representations for how the individual processes are

parametrized in such models. Vmax, maximum phytoplankton growth rate; KN, nutrient half saturation concentration; g , maximum

zooplankton growth rate; KP, half saturation concentration for phytoplankton grazing; gZ, zooplankton assimilation efficiency; lP,

phytoplankton mortality rate; lZ, zooplankton mortality rate; mP, fraction of dead phytoplankton nitrogen that is remineralized in the

euphotic zone; mZ, as mP, but for zooplankton. Adapted from Sarmiento JL and Gruber N (2006) Ocean Biogeochemical Dynamics,

526pp. Princeton, NJ: Princeton University Press.


Nn

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mm

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NT (mmol m–3) NT (mmol m–3)

NP-model(a) (b)

NPZ-model

Figure 8 Nitrogen in phytoplankton (P), zooplankton (Z), and nitrate (Nn) as a function of total nitrogen. (a) Results from a two-

component model that just includes N and P. (b) Results from a three-component model that is akin to that shown in Figure 7(b). The

vertical axis is concentration in each of the components plotted as the cumulative amount. Adapted from Sarmiento JL and Gruber N

(2006) Ocean Biogeochemical Dynamics, 526pp. Princeton, NJ: Princeton University Press.


large phytoplankton that dominate the highly pro-ductive upwellling regions are represented with asingle group, whose growth characteristics cannotsimultaneously represent both. An additional chal-lenge of the large-scale coupling problem is theinteraction of oceanic circulation/mixing with themarine ecological and biogeochemical processes.Often, small deficiencies in the physical model getamplified by the ecological/biogeochemical model, sothat the resulting fields of phytoplankton abundancemay diverge strongly from observations.

The latter problem is addressed by improvingcritical aspects of the physical model, such as upperocean mixing, atmospheric forcing, resolution, andnumerical tracer transport algorithms, while thefirst problem is addressed by the consideration ofdistinct plankton functional groups. These functionalgroups distinguish themselves by their differentsize, nutrient requirement, biogeochemical role,and several other characteristics, but not necessarilyby their taxa. Currently existing models typi-cally consider the following phytoplankton func-tional groups: small phytoplankton (nano- andpicoplankton), silicifying phytoplankton (diatoms),calcifying phytoplankton (coccolithophorids), N2-fixing phytoplankton, large (nonsilicifying) phyto-plankton (e.g., dinoflagellates and phaeocystis), withthe choice of which group to include being driven bythe particular question at hand. The partial differ-ential equations for the different phytoplanktonfunctional groups are essentially the same and followa structure similar to [9], but are differentiated byvarying growth parameters, nutrient/light require-ments, and susceptibility to grazing. At present,most applications include between five and 10

phytoplankton functional groups. Some recentstudies have been exploring the use of several dozenfunctional groups, whose parameters are generatedstochastically with some simple set of rules that arethen winnowed via competition for resources amongthe functional groups. Since the different phyto-plankton functional groups are also grazed differ-entially, different types of zooplankton generallyneed to be considered as well, though fully developedmodels with diverse zooplankton functional groupsare just emerging. An alternative is to use a singlezooplankton group, but with changing grazing/growth characteristics depending on its main foodsource. A main advantage of models that build onthe concept of plankton functional groups is theirability to switch between different phytoplanktoncommunity structures and to simulate their differ-ential impact on marine biogeochemical processes.For example, the nutrient poor subtropical gyrestend to be dominated by nano- and picoplankton,whose biomass tends to be tightly capped by grazingby very small zooplankton. This prevents the groupforming blooms, even under nutrient-rich conditions.By contrast, larger phytoplankton, such as diatoms,can often escape grazing control (at least tempora-rily) and form extensive blooms. Such phytoplanktoncommunity shifts are essential for controlling theexport of organic matter toward the abyss, since theexport ratio, that is, the fraction of net primaryproduction that is exported, tends to increase sub-stantially in blooms.

Results from the coupling of such a multiplefunctional phytoplankton ecosystem model and of arelatively simple biogeochemical model to a global3-D circulation model show substantial success in


representing the basic features of chlorophyll, air–seaCO2 flux, and surface nutrient concentration(Figure 9) seen in the observations (Figure 2). Thecomparison also shows some clear deficiencies, suchas the lack of the representation of the highly ele-vated chlorophyll concentrations associated withmany continental boundaries. This deficiency is

80° S

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Chlorophyll (mg Chl m−3)

Nitrate (mmol m−3)

Sea-to-air CO2 flux (mol m−2 yr−1)

(a)

(b)

(c)

Figure 9 Global maps of model simulated key biogeochemica

Atmospheric Research (NCAR) Community Climate System Model

(mg Chl m� 3); (b) annual mean surface distribution of nitrate (mmol

period 1990 until 2000. All model results stem from a simulation, in w

to a global 3-D ocean circulation model. Results provided by S.C.

mostly a result of the lack of horizontal resolution.This could be overcome, theoretically, by increas-ing the resolution of the global models to theeddy-resolving scale needed to properly representsuch boundary regions (c. 5–10 km or so, rather thanthe several hundred kilometer resolution currentlyused for most global-scale biogeochemical/ecological

160° W 40° W120° W 80° W GM60° E

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l/ecological targets (cf. Figure 2) from the National Center for

(CCSM): (a) annual mean distribution of near-surface chlorophyll�3); and (c) annual mean air–sea CO2 flux (mol m� 2 yr� 1) for the

hich a multiple functional phytoplankton group model was coupled

Doney and I. Lima, WHOI.

34.6° N

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0 0.80.4 1.2 2 2.4 2.8 3.2 3.6 4 15 0.1 0.17 0.29 0.5 0.87 1.5 2.5 4.41.6

Nitrate (mmol−3) Chlorophyll (mg m−3)

(a) (b)

Figure 10 Snapshots of (a) surface nitrate and (b) surface chlorophyll as simulated by a 1-km, that is, eddy-resolving, regional

model for the Southern California Bight. The snapshots represent typical conditions in response to a spring-time upwelling event in this

region. The model consists of a multiple phytoplankton functional group model that has been coupled to the Regional Ocean Modeling

System (ROMS). Results provided by H. Frenzel, UCLA.


simulations). This is currently feasible for only veryshort periods, so that limited domain models areoften used instead.

Eddy-resolving Regional Models

Limited domain models, as shown in Figure 10 forthe Southern California Bight, that is, the southern-most region of the West Coast of the US, can be runat much higher resolutions over extended periods,permitting the investigation of the processes occur-ring at the kilometer scale. The most important suchprocesses are meso- and submesoscale eddies andother manifestations of turbulence, which are ubi-quitous features of the ocean. The coupling of thesame ecosystem/biogeochemical model used for theglobal model shown in Figure 9 to a 1-km resolutionmodel of the Southern California Bight reveals thespatial richness and sharp gradients that are com-monly observed (Figure 10) and that emerge from theintense interactions of the physical and biogeo-chemical/ecological processes at the eddy scale. Sincesuch mesoscale processes are unlikely to be resolvedat the global scale for a while, a current challenge isto find parametrizations that incorporate the netimpact of these processes without actually resolvingthem explicitly.

Future Directions

The modeling of marine biogeochemical/ecologicalprocesses is a new and rapidly evolving field, so that

predictions of future developments are uncertain.Nevertheless, it is reasonable to expect that modelswill continue to evolve along the major axes ofcomplexity, including, for example, the consider-ation of higher trophic levels (Figure 4). One alsoenvisions that marine biogeochemical/ecologicalmodels will be increasingly coupled to other systems.A good example are Earth System Models that at-tempt to represent the entire climate system of theEarth including the global carbon cycle. In thosemodels, the marine biogeochemical/ecological mod-els are just a small part, but interact with all othercomponents, possibly leading to complex behaviorincluding feedbacks and limit cycles. Another majoranticipated development is the increasing use of in-verse modeling approaches to optimally make use ofthe increasing flow of observations.

Glossary

advection The transport of a quantity in a vectorfield, such as ocean circulation.

anthropogenic carbon The additional carbon thathas been released to the environment over the lastseveral centuries by human activities includingfossil-fuel combustion, agriculture, forestry, andbiomass burning.

biogeochemical loop, great A set of key processesthat control the distribution of bioreactiveelements in the ocean. The loop starts with thephotosynthetic production of organic matter in thelight-illuminated upper ocean, a fraction of which


is exported to depth mostly by sinking of particles.During their sinking in the dark deeper layers ofthe ocean, this organic matter is consumed bybacteria and zooplankton that transform it back toits inorganic constituents while consuming oxi-dized components in the water (mostly oxygen).The great biogeochemical loop is closed by thephysical transport and mixing of these inorganicbioreactive elements back to the near-surfaceocean, where the process starts again. This greatbiogeochemical loop also impacts the distributionof many other elements, particularly those that areparticle reactive, such as thorium.

coccolithophorids A group of phytoplanktonbelonging to the haptophytes. They are distingui-shed by their formation of small mineral calciumcarbonate plates called coccoliths, which contri-bute to the majority of marine calcium carbonateproduction. An example of a globally significantcoccolithophore is Emiliania huxleyi.

diatoms A group of phytoplankton belonging tothe class Bacillariophyceae. They are one of themost common types of phytoplankton anddistinguish themselves through their productionof a cell wall made of amorphous silica, calledopal. These walls show a wide diversity in form,but usually consist of two symmetrical sides with asplit between them.

diffusion The transport of a quantity by Brownianmotion (molecular diffusion) or turbulence (eddydiffusion). The latter is actually some form ofadvection, but since its net effect is akin todiffusion, it is often represented as a diffusiveprocess.

export production The part of the organic matterformed in the surface layer by photosynthesis thatis transported out of the surface layer and into theinterior of the ocean by particle sinking, mixing,and circulation, or active transport by organisms.

models, concentration based Models, in which thebiological state variables are given as numbers perunit volume, that is, concentration. This approachis often used when physical dispersion plays animportant role in determining the biological andbiogeochemical impact of these state variables.Concentration-based models are most often usedto represent lower trophic levels in the ocean.

models, forward Models, in which time isintegrated forward to compute the temporalevolution of the distribution of state variables inresponse to a set of initial and boundaryconditions.

models, individually based Models, in which thebiological state variables represent individualorganisms or a small group of individual

organisms. This approach is often used when lifecycles play a major role in the development ofthese organisms, such as is the case for mostmarine organisms at higher trophic levels.

models, inverse Models that aim to optimallycombine observations with knowledge about theworkings of a system as embodied in the model.Solutions to such inverse models can be improvedestimates of the current state of the system (stateestimation), improved estimates of the initial orboundary conditions, or an optimal set ofparameters. A typical example of an inversemodel is the optimal determination of ecologicalparameters, such as growth and grazing rates,given, for example, the observed distribution ofphytoplankton, zooplankton, and nutrients.

net primary production Rate of net fixation ofinorganic carbon into organic carbon byautotrophic phytoplankton. This net rate is thedifference between the gross uptake of inorganiccarbon during photosynthesis and autotrophicrespiration.

organisms, autotrophic An autotroph (from theGreek autos¼ self and trophe¼ nutrition) is anorganism that produces organic compounds fromcarbon dioxide as a carbon source, using eitherlight or reactions of inorganic chemicalcompounds, as a source of energy. An autotrophis known as a producer in a food chain.

organisms, heterotrophic A heterotroph (Greekheterone¼ (an)other and trophe¼ nutrition) is anorganism that requires organic substrates to get itscarbon for growth and development. Aheterotroph is known as a consumer in the foodchain.

plankton Organisms whose swimming speed issmaller than the typical speed of ocean currents,so that they cannot resist currents and are henceunable to determine their horizontal position. Thisis in contrast to nekton organisms that can swimagainst the ambient flow of the water environmentand control their position (e.g., squid, fish, krill,and marine mammals).

plankton, phytoplankton Phytoplankton are the(photo)autotrophic components of the plankton.Phytoplankton are pro- or eukaryotic algae thatlive near the water surface where there is sufficientlight to support photosynthesis. Among the moreimportant groups are the diatoms, cyanobacteria,dinoflagellates, and coccolithophorids.

plankton, zooplankton Zooplankton are hetero-trophic plankton that feed on other plankton.Dominant groups include small protozoansor metazoans (e.g., crustaceans and otheranimals).


See also

Biogeochemical Data Assimilation. Carbon Cycle.Carbon Dioxide (CO2) Cycle. Forward Problem inNumerical Models. Inverse Modeling of Tracersand Nutrients. Mesoscale Eddies. Nitrogen Cycle.Ocean Carbon System, Modeling of. OceanCirculation. Phosphorus Cycle.

Further Reading

DeYoung B, Heath M, Werner F, Chai F, Megrey B, andMonfray P (2004) Challenges of modeling ocean basinecosystems. Science 304: 1463--1466.

Doney SC (1999) Major challenges confronting marinebiogeochemical modeling. Global BiogeochemicalCycles 13(3): 705--714.

Fasham M (ed.) (2003) Ocean Biogeochemistry. NewYork: Springer.

Fasham MJR, Ducklow HW, and McKelvie SM (1990) Anitrogen-based model of plankton dynamics in theoceanic mixed layer. Journal of Marine Systems 48:591--639.

Glover DM, Jenkins WJ, and Doney SC (2006) Course No.12.747: Modeling, Data Analysis and NumericalTechniques for Geochemistry. http://w3eos.whoi.edu/12.747 (accessed in March 2008).

Rothstein L, Abbott M, Chassignet E, et al. (2006)Modeling ocean ecosystems: The PARADIGM Program.Oceanography 19: 16--45.

Sarmiento JL and Gruber N (2006) Ocean BiogeochemicalDynamics, 526pp. Princeton, NJ: Princeton UniversityPress.

Relevant Websites

http://www.uta.edu– Interactive models of ocean ecology/biogeochemistry.

http://w3eos.whoi.edu/12.747

http://w3eos.whoi.edu/12.747

http://www.uta.edu

ocean biogeochemistry and ecology, modeling of

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